In this paper, we focus on finite cyclic groups. Following the notations from [1]}, write \(S-T(G)\)  (respectively, \(T-S(G)\) ), if the “Spectral \(\Rightarrow \)  Tile” (respectively, “Tile \(\Rightarrow \)  Spectral”) direction of Fuglede's conjecture holds in \(G\) . Then we have the following relations [2]}, [1]}:
\(T-S(\mathbb {R})\Leftrightarrow T-S(\mathbb {Z})\Leftrightarrow T-S(\mathbb {Z}_{N})\text{ for all }N,\) 
